Question

A nucleus ( mass no. 238 ) initially at rest into another nucleus ( mass no 234 ) emitting an $\alpha$ particle (mass no-4) with the speed of$1.17\times {10}^7$m/sec. Find the recoil speed of the remaining nucleus.

Answer 1

the nucleus was at rest initially.

so, it has momentum $=0$

as,man of $\alpha$-particle has speed $V_1=1.17\times {10}^{7}m/s$

from conservation of momentum $m_1{v}_1+m_2{v}_2=0$

$v_2=\frac{-m_1{v}_1}{m_2}$=$\frac{-4\times 1.17\times {10}^7}{234}=-2\times {10}^{5}m/s$

$\therefore$ recoil velocity of nucleus = $2\times {10}^{5}m/s.$